# Solved (Free): New born elephant calves usually weigh between 200 and 250 pounds until october 2006

#### ByDr. Raju Chaudhari

Apr 12, 2021

Newborn Elephant Weights. New born elephant calves usually weigh between 200 and 250 pounds until october 2006, that is. an asian elephant at the Houston (Texas) zoo gave birth to a male calf weighing in at a whopping 384 pounds! Mack (like the truck) is believed to believed to be the heaviest elephant calf ever born at a facility accredited by the association of zoos and aquariums. If, indeed, the mean weight for new born elephant calves is 225 pounds with a standard deviation of 45 pounds, what is the probability of a newborn weighing at least 384 pounds? Assume that the weights of newborn elephants are normally distributed.

#### Solution

Let $X$ denote the weight for newborn calves.

Given that $X\sim N(225, 45^2)$. That is $\mu= 225$ and $\sigma =45$.

We want to find the probability of a newborn weighing at least 384 pounds.

The $Z$ score corresponding to $384$ is

 \begin{aligned} z&=\frac{384-\mu}{\sigma}\\ &=\frac{384 - 225}{45}\\ &= 3.53 \end{aligned}

The probability of a newborn weighing at least 384 pounds is

 \begin{aligned} P(X\geq 384) &= 1-P\bigg(\frac{X-\mu}{\sigma} < \frac{384-225}{45}\bigg)\\ &= 1-P\bigg(Z < 3.53\bigg)\\ &=1-0.9998\\ &=0.0002 \end{aligned}